12th Mathematics - Book Back Answers - Chapter 4 - English Medium Guides

  

 

Plus Two / 12th Mathematics - Book Back Answers - Chapter 4 - English Medium

Tamil Nadu Board 12th Standard Mathematics - Chapter 4: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 4 from the Tamil Nadu State Board 12th Standard Chemistry textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 4 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 12 students! Prepare well and aim for top scores. Thank you!

 

I. Multiple Choice Questions

1. The value of sin⁻¹  (cos x), 0 ≤ x ≤ 𝜋 is
(1) 𝜋-x
(2) x-$\frac{\mathbf{\pi }}{\mathbf{2}}$
(3) $\frac{\mathbf{\pi }}{\mathbf{2}}$-x
(4) x-𝜋
Answer Key:

2. If sin⁻¹x + sin⁻¹y= $\frac{\mathbf{2}\mathbf{\pi }}{\mathbf{3}}$ ; then cos⁻¹ x + cos⁻¹ y is equal to
(1) $\frac{\mathbf{2}\mathbf{\pi }}{\mathbf{3}}$
(2) $\frac{\mathbf{\pi }}{\mathbf{3}}$
(3) $\frac{\mathbf{\pi }}{\mathbf{6}}$
(4) 𝜋
Answer Key:

3. sin⁻¹$\frac{\mathbf{3}}{\mathbf{5}}$ − cos⁻¹$\frac{\mathbf{12}}{\mathbf{13}}$ + sec⁻¹$\frac{\mathbf{5}}{\mathbf{3}}$ cosec⁻¹$\frac{\mathbf{13}}{\mathbf{12}}$ is equal to
(1) 2$\frac{\mathbf{\pi }}{}$ 
(2) $\frac{\mathbf{\pi }}{}$ 
(3) 0 
(4) tan⁻¹ $\frac{\mathbf{12}}{\mathbf{65}}$
Answer Key:

4. If sin⁻¹ x = 2sin⁻¹𝞪 has a solution, then
(1) |𝞪| ≤$\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}$

(2) |𝞪|≥$\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}$
(3) |𝞪|<$\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}$
(4) |𝞪|>$\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}$
Answer Key:

5. sin⁻¹(cos x ) = $\frac{\mathbf{\pi }}{\mathbf{2}}$ − x p x is valid for
(1) - $\frac{\mathbf{\pi }}{}$ ≤ x ≤ 0
(2) 0 ≤ x ≤ $\frac{\mathbf{\pi }}{}$
(3) -$\frac{\mathbf{ \pi }}{\mathbf{2 }}$≤ x ≤ $\frac{\mathbf{\pi }}{\mathbf{2}}$
(4) - $\frac{\mathbf{\pi }}{\mathbf{4}}$ ≤ x ≤ $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{4}}$
Answer Key:

6. If sin⁻¹ x + sin⁻¹y + sin⁻¹z = $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{2}}$, the value of x²⁰¹⁷ + y²⁰¹⁸ + z²⁰¹⁹- $\frac{\mathbf{9}}{{\mathbf{x}}^{\mathbf{101}}\mathbf{+}{\mathbf{y}}^{\mathbf{101}}\mathbf{+}{\mathbf{z}}^{\mathbf{101}}}$ is
(1) 0 
(2) 1 
(3) 2 
(4) 3
Answer Key:

7. If cot⁻¹ = $\frac{\mathbf{2}\mathbf{\pi }}{\mathbf{5}}$ for some x∈R , the value of tan⁻¹ x is
(1) -$\frac{\mathbf{\pi }}{\mathbf{10}}$
(2) $\frac{\mathbf{\pi }}{\mathbf{5}}$
(3) $\frac{\mathbf{\pi }}{\mathbf{10}}$
(4) -$\frac{\mathbf{\pi }}{\mathbf{5}}$
Answer Key:

8. The domain of the function defined by f (x) = sin⁻¹ $\sqrt{\mathbf{x}\mathbf{-}\mathbf{1}}$ is
(1) [1, 2] 
(2) [−1, 1] 
(3) [0, 1] 
(4) [−1, 0]
Answer Key:

9. If x = $\frac{\mathbf{1}}{\mathbf{5}}$, the value of cos (cos⁻¹ x + 2sin⁻¹ x) is
(1) -$\sqrt{\frac{\mathbf{24}}{\mathbf{25}}}$
(2) $\sqrt{\frac{\mathbf{24}}{\mathbf{25}}}$
(3) $\frac{\mathbf{1}}{\mathbf{5}}$
(4) -$\frac{\mathbf{1}}{\mathbf{5}}$
Answer Key:

10. tan⁻¹+ tan⁻¹is equal to 
(1) $\frac{\mathbf{1}}{\mathbf{2 }}$cos⁻¹

(2) $\frac{\mathbf{1}}{\mathbf{2}}$sin⁻¹
(3) $\frac{\mathbf{1}}{\mathbf{2tan}}$⁻¹
(4) $\frac{\mathbf{tan}}{}$⁻¹
Answer Key:

11. If the function f (x) = sin⁻¹ (x² − 3), then x belongs to
(1) [-1, 1]
(2) [$\sqrt{\mathbf{2}}$, 2]
(3) [-2, -$\sqrt{\mathbf{2}}$ ]∪[$\sqrt{\mathbf{2}}$ , 2]
(4) [-2, - $\sqrt{\mathbf{2}}$]
Answer Key:

12. If cot-1 2 and cot-1 3 are two angles of a triangle, then the third angle is
(1)
(2)
(3)
(4)
Answer Key:

13. sin− tan sin− _
. Then x is a root of the equation
(1) x2 −x−6=0 
(2) x2 −x−12=0 
(3) x2 +x−12=0 
(4) x2 +x−6=0

Answer Key:

 
14. sin−1 (2cos2 x −1)+ cos−1 (1− 2sin2 x) =
(1) 
(2) 
(3) 
(4) 
Answer Key:

15. If cot−1 ( sinα )+tan−1 ( sinα )=u , then cos 2u is equal to
(1) tan2 α 
(2) 0 
(3) -1 
(4) tan 2α
Answer Key:

16. If x £1, then 2 2
to
(1) tan-1 x 
(2) sin-1 x 
(3) 0 
(4) p
Answer Key:

17. The equation tan− − cot− = tan− _
 (1) no solution 
(2) unique solution
(3) two solutions 
(4) infinite number of solutions
Answer Key:

18. If sin− + cot− _
, then x is equal to
(1) 
(2) 
(3) 
(4) 
Answer Key:

19. If sin−1 + −1 =
cosec−1
, then the value of x is
(1) 4 
(2) 5 
(3) 2 
(4) 3
Answer Key:

20. sin(tan−1 x), | x |<1 is equal to
(1)
(2)
(3)
 4)
Answer Key:

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics